## _wp0846

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### Introduction — recent growth context and research questions
- Real GDP growth averaged less than 3 percent over 1991–2003.
- Real GDP growth accelerated to 5½ percent in 2004–06.
- Growth in the year ending June 2007 was close to 8 percent.
- Private investment rose from 9 percent of GDP in 2002 to 19 percent of GDP in 2006.
- External conditions cited as favorable: strong global growth, improving terms of trade, abundant international liquidity, and low interest rates.
- Paper’s main questions:
  - To what extent was growth driven by external factors vis-à-vis domestic ones?
  - How sensitive is Colombian growth to changes in external conditions?
- Methodological approach: Bayesian VAR (BVAR) with informative steady-state priors (Villani, 2008).
- Empirical exercises: impulse response functions, variance decomposition, historical decomposition, out-of-sample forecasting comparisons, and conditional forecasts under alternative external scenarios.

### Model specification and priors
- Model form: (L)η ψ x G = −t t t (equation (1) in source).
- x_t is an n×1 vector of stationary macroeconomic variables; η_t is an n×1 iid error vector with E(η_t)=0 and E(η_t η_t′)=Σ.
- ψ provides the steady state; informative priors can be placed on ψ.
- Priors:
  - Prior on Σ: ∝ Σ^(−(n+p+1)/2) (non-informative).
  - Prior on vec(G): vec(G) ~ N(θ_G, Ω_G).
  - Prior on ψ: ψ ~ N(θ_ψ, Ω_ψ).
- Minnesota-type prior on dynamics:
  - Prior mean on first own lag = 0.9 if variable in levels and 0 if in growth rates.
  - Other coefficients prior mean = 0.
  - Modification to standard Minnesota prior because a prior mean of 1 on first own lag is inconsistent with mean-adjusted model.

### Empirical implementation — variables, sample, and steady-state priors
- Variable vector x_t (order shown in equation (2)):
  - Δ world_t y = log of world real GDP (excluding Colombia) (growth).
  - US_t i = nominal three-month U.S. treasury bill rate.
  - EMBI_t = JP Morgan emerging market bond index spread for Latin America (excluding Colombia).
  - HY_t = high-yield corporate bond spread in the United States.
  - FDI_t = foreign direct investment as a share of GDP (proxy for investment climate).
  - g_t = logarithm of real government spending (growth).
  - y_t = logarithm of Colombia’s real GDP (growth).
  - i_t = nominal bank lending rate in Colombia.
- Steady-state priors based on theory, empirical studies, WEO Fall 2007 projections, and literature.
- Prior for FDI specified with a relatively wide distribution.
- Prior on lending rate reasonably wide.
- Lag length set to 2 = p.
- Sample: quarterly data from 1995Q2 to 2007Q2.
- Table 1. 95 percent prior probability intervals for parameters determining steady-state values:
  - (3.75, 4.75)
  - (3.00, 5.00)
  - (2.00, 5.00)
  - (3.00, 6.00)
  - (3.00, 5.00)
  - (4.25, 5.25)
  - (4.25, 5.25)
  - (8.00, 16.00)

### Impulse responses — identification and shock magnitudes
- Identification via standard Cholesky decomposition with variables ordered as in x_t.
- Impulse responses from one-standard-deviation shocks.
- One-standard-deviation shock magnitudes reported:
  - global growth: 0.32 percentage points
  - U.S. treasury bill rate: 30 basis points
  - EMBI spread: 147 basis points
  - high yield bond spread: 43 basis points
- Baseline numeric summary reported in source:
  - 1.25 percentage points for FDI
  - 2.09 percentage point for public spending growth
  - 0.70 percentage points for Colombian GDP growth
  - 165 basis points for the domestic interest rate

### Impulse-response findings and sensitivity of Colombian GDP growth
- Global growth:
  - If global growth has fallen by one percentage point four quarters after the shock, Colombian GDP growth has at the same time fallen roughly by 1.4 percentage points.
  - Effects operate through trade channels and via changes in external financial conditions (EMBI and high-yield spreads).
- External financial conditions:
  - An increase of 100 basis points in the EMBI spread would lower Colombian GDP growth by roughly 0.3 percentage points after the first year.
  - A 100 basis point shock to the high-yield spread would cause Colombian GDP growth to fall by approximately 0.2 percentage points (effect substantially larger at shorter horizons).
  - A shock to the U.S. interest rate has a small impact on Colombian growth; the domestic lending-rate response to U.S. rate shocks is statistically insignificant.
- Domestic variables:
  - A one percentage point increase in the ratio of FDI to GDP raises Colombian GDP growth by roughly 0.56 percentage point after one year.
  - A one percent increase in public spending raises GDP growth by 0.36 percentage points (Keynesian short-run effect).
  - An increase of 100 basis points in the lending rate reduces GDP growth by close to 0.3 percentage point after one year.

### Variance decomposition — contributions to Colombian GDP growth
- Aggregate shares:
  - External factors account for about 40 percent of the variance.
  - Domestic factors account for about 60 percent of the variance.
- Major contributors at the 20-quarter horizon (apart from own shocks):
  - World GDP growth: about 17 percent.
  - Government spending: about 16 percent.
  - FDI: about 14 percent.
- Other contributors:
  - U.S. interest rate, EMBI spread, and high-yield bond spread: each around 10 percent.
  - Domestic monetary policy (lending rate): explains only three percent of Colombian growth.
- Caveat: classification between domestic and foreign influences is imperfect; some domestic variables may reflect foreign influences and could overstate domestic roles.

### Historical decomposition (2004–07)
- Foreign shocks:
  - Model suggests foreign shocks were not particularly favorable in 2004 and 2005; foreign shocks became positive for Colombian GDP growth only in late 2006.
  - The model’s endogenous forecast of the external environment was itself optimistic, affecting interpretation.
- FDI (investment climate):
  - Changes in the investment climate were consistently positive during 2004–07, providing a stimulus to the economy.
- Fiscal and monetary policy shocks:
  - Positive at the beginning of the period but less favorable from early 2006.
- Colombian-growth-only shocks:
  - Show an opposite pattern to macroeconomic policy shocks in the model’s decomposition.

### Out-of-sample forecasting performance
- Models compared: mean-adjusted BVAR with informative priors, conventional BVAR (non-informative prior for Φ), and a naïve forecast.
- Evaluation setup:
  - Models estimated using data from 1995Q2 to 2002Q4 to forecast to 2004Q4 (eight quarters ahead), recursively expanding the sample and re-forecasting.
  - Last evaluation: model estimated from 1995Q2 to 2007Q1 and forecast one period ahead.
- Results (RMSE-based):
  - The mean-adjusted BVAR almost always outperforms the conventional BVAR and the naïve forecast (relative RMSE < 1) for most variables.
  - Exception: lending rate — the mean-adjusted BVAR is consistently outperformed by the naïve forecast.

### Unconditional and conditional forecasts through 2010 — scenarios and outcomes
- Forecast types:
  - Unconditional (endogenous) forecast: model-based.
  - Conditional forecasts:
    - WEO-based conditional forecast: imposes world growth path (IMF Fall 2007 WEO) and U.S. interest-rate path.
    - Downside hypothetical conditional forecast: global growth lower than Fall 2007 WEO by 1 percentage point in each quarter of 2008; U.S. three-month treasury bill rate decreases in response.
- Key forecast outcomes:
  - Unconditional (endogenous) forecast:
    - Growth decelerates to around 4½ percent by end-2008 and stabilizes at about 4 percent in 2009.
  - WEO-based conditional forecast:
    - Growth of about 5¼ percent by the end of 2008 and 4¾ percent in late 2009.
  - Downside conditional forecast (global growth shock):
    - Colombian GDP growth reaches a low of 3 percent in late 2008Q3 (compared to 4¾ percent under the WEO-based conditional forecast).
    - Under this scenario growth declines to 3 percent, which is 1¾ percentage points below the baseline forecast.
    - EMBI spread increases substantially (not conditioned upon), consistent with historical correlation between U.S. downturns and global risk appetite.
    - Recovery predicted to be fairly rapid, with growth reaching the same level as in the WEO-based forecast by the end of 2009.
- Interpretation:
  - Colombian growth is fairly sensitive to changes in global growth.
  - A moderate global slowdown would produce a substantial domestic slowdown but not a full-blown recession; growth remains positive and the downturn is mild by historical standards.

### Conclusions and policy-relevant findings
- Aggregate findings:
  - Domestic factors explain about 60 percent of Colombian GDP growth variability; external developments explain about 40 percent.
  - Among domestic factors, the investment climate (FDI) and fiscal policy are prominent contributors; monetary policy has had a small contribution.
  - Global economic growth is the single most important external factor for Colombian growth.
  - External financial-condition measures (U.S. interest rate, EMBI, high-yield spreads) each account for only modest shares.
- Policy implications and robustness considerations:
  - Fiscal and monetary policy shocks each have moderate short-run impacts on growth; investment-climate improvements have a moderate positive effect.
  - The model implies a deceleration of economic growth to 4-5 percent in 2008-10, from close to 7 percent in 2006-07.
  - Structural reforms since the early 2000s, higher international reserves, and a flexible exchange rate regime may have enhanced resilience to external shocks, but greater financial integration could increase sensitivity; the net effect remains to be tested.
  - Results are sensitive to sample period and included variables; classification between domestic and foreign influences is imperfect.

* _wp0846 - 1.   Data (PDF chapter/section) — content from https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0846.pdf *

### 1.   Data ..............................................................................................................

### 1.   Data

### Introduction — recent growth context
- Real GDP growth averaged less than 3 percent over 1991–2003.
- Real GDP growth accelerated to 5½ percent in 2004–06.
- Growth in the year ending June 2007 was close to 8 percent.
- Private investment rose from 9 percent of GDP in 2002 to 19 percent of GDP in 2006.
- External conditions cited as favorable: strong global growth, improving terms of trade, abundant international liquidity, and low interest rates.
- Paper’s main questions:
  - To what extent was growth driven by external factors vis-à-vis domestic ones?
  - How sensitive is Colombian growth to changes in external conditions?
- Methodological approach: Bayesian VAR (BVAR) with informative steady-state priors (Villani, 2008) to reduce degrees-of-freedom issues and improve forecasting performance.
- Empirical exercises include impulse response functions, variance decomposition, historical decomposition (Adolfson et al., 2007), out-of-sample forecasting comparisons, and conditional forecasts under alternative external scenarios.

### The model — specification and priors
- Model form: (L)η ψ x G = −t t t (equation (1) in source).
- x_t is an n×1 vector of stationary macroeconomic variables; η_t is an n×1 iid error vector with E(η_t)=0 and E(η_t η_t′)=Σ.
- ψ provides the steady state; informative priors can be placed on ψ.
- Priors:
  - Prior on Σ: ∝ Σ^(−(n+p+1)/2) (non-informative).
  - Prior on vec(G): vec(G) ~ N(θ_G, Ω_G).
  - Prior on ψ: ψ ~ N(θ_ψ, Ω_ψ).
- Minnesota-type prior on dynamics: prior mean on first own lag = 0.9 if variable in levels and 0 if in growth rates; other coefficients prior mean = 0. (Modification to standard Minnesota prior because a prior mean of 1 on first own lag is inconsistent with mean-adjusted model.)

### Empirical implementation — variables, sample, and steady-state priors
- Variable vector x_t (order shown in equation (2)):
  - Δ world_t y = log of world real GDP (excluding Colombia) (growth).
  - US_t i = nominal three-month U.S. treasury bill rate.
  - EMBI_t = JP Morgan emerging market bond index spread for Latin America (excluding Colombia).
  - HY_t = high-yield corporate bond spread in the United States.
  - FDI_t = foreign direct investment as a share of GDP (proxy for investment climate).
  - g_t = logarithm of real government spending (growth).
  - y_t = logarithm of Colombia’s real GDP (growth).
  - i_t = nominal bank lending rate in Colombia.
- Steady-state priors based on theory, empirical studies, WEO Fall 2007 projections (for world GDP growth), and literature (Taylor (1993), Clarida et al. (1998), Österholm and Zettelmeyer (2008), Loayza et al. (2004), Zettelmeyer (2006)).
- Prior for FDI specified with a relatively wide distribution due to weak guidance from theory/literature.
- Prior on lending rate reasonably wide to reflect uncertainty.
- Lag length set to 2 = p.
- Sample: quarterly data from 1995Q2 to 2007Q2.
- Table 1. 95 percent prior probability intervals for parameters determining steady-state values:
  - (3.75, 4.75)
  - (3.00, 5.00)
  - (2.00, 5.00)
  - (3.00, 6.00)
  - (3.00, 5.00)
  - (4.25, 5.25)
  - (4.25, 5.25)
  - (8.00, 16.00)

### Results — impulse responses and variance decomposition (overview)
- Focus in text: Colombian GDP growth impulse responses and variance decomposition; full set in Appendix Figures A1 and A2.
- Impulse responses generated from one-standard-deviation shocks.
- Identification via standard Cholesky decomposition with variables ordered as in x_t (equation (2)).
- One-standard deviation shock magnitudes reported:
  - global growth: 0.32 percentage points
  - U.S. treasury bill rate: 30 basis points
  - EMBI spread: 147 basis points
  - high yield bond spread: 43 basis points

*Italic source attribution: _wp0846 - 1.   Data (PDF chapter/section) — content from https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0846.pdf*

### 1.25  percentage  points  for  FDI,  2.09  percentage  point  for  public  spending  growth,  0.70  percentage  points  

### _wp0846 - 1.25  percentage  points  for  FDI,  2.09  percentage  point  for  public  spending  growth,  0.70  percentage  points

### Impulse responses and sensitivity of Colombian GDP growth
- Baseline numeric summary from the source: 1.25 percentage points for FDI, 2.09 percentage point for public spending growth, 0.70 percentage points for Colombian GDP growth and 165 basis points for the domestic interest rate.
- Global growth:
  - If global growth has fallen by one percentage point four quarters after the shock, Colombian GDP growth has at the same time fallen roughly by 1.4 percentage points.
  - Global growth effects operate through trade channels and via changes in external financial conditions (EMBI and high-yield spreads).
- External financial conditions:
  - An increase of 100 basis points in the EMBI spread would lower Colombian GDP growth by roughly 0.3 percentage points after the first year.
  - A 100 basis point shock to the high-yield spread would cause Colombian GDP growth to fall by approximately 0.2 percentage points (effect substantially larger at shorter horizons).
  - A shock to the U.S. interest rate has a small impact on Colombian growth; the domestic lending-rate response to U.S. rate shocks is statistically insignificant.
- Domestic variables:
  - A one percentage point increase in the ratio of FDI to GDP raises Colombian GDP growth by roughly 0.56 percentage point after one year.
  - A one percent increase in public spending raises GDP growth by 0.36 percentage points (Keynesian short-run effect).
  - An increase of 100 basis points in the lending rate reduces GDP growth by close to 0.3 percentage point after one year.

### Variance decomposition (contributions to Colombian GDP growth)
- Aggregate shares:
  - External factors account for about 40 percent of the variance.
  - Domestic factors account for about 60 percent of the variance.
- Major contributors at the 20-quarter horizon (apart from own shocks):
  - World GDP growth: about 17 percent.
  - Government spending: about 16 percent.
  - FDI: about 14 percent.
- Other contributors:
  - U.S. interest rate, EMBI spread, and high-yield bond spread: each around 10 percent.
  - Domestic monetary policy (lending rate): explains only three percent of Colombian growth.
- Caveats:
  - Breaking down contributions into domestic vs. foreign is not straightforward; some domestic variables (investment climate, government spending) may reflect foreign influences, potentially overstating domestic roles.

### Historical decomposition (2004–07)
- Foreign shocks:
  - The model suggests foreign shocks were not particularly favorable in 2004 and 2005; foreign shocks became positive for Colombian GDP growth only in late 2006.
  - The model’s endogenous forecast of the external environment was itself optimistic, which affects interpretation.
- FDI (investment climate):
  - Changes in the investment climate were consistently positive during 2004–07, providing a stimulus to the economy (consistent with improved domestic security and economic policies).
- Fiscal and monetary policy shocks:
  - Positive at the beginning of the period but less favorable from early 2006.
- Colombian-growth-only shocks:
  - Show an opposite pattern to macroeconomic policy shocks in the model’s decomposition.

### Out-of-sample forecasting performance
- Models compared: mean-adjusted BVAR with informative priors, conventional BVAR (non-informative prior for Φ), and a naïve forecast.
- Evaluation setup:
  - Models estimated using data from 1995Q2 to 2002Q4 to forecast to 2004Q4 (eight quarters ahead), recursively expanding the sample and re-forecasting.
  - Last evaluation: model estimated from 1995Q2 to 2007Q1 and forecast one period ahead.
- Results (RMSE-based):
  - The mean-adjusted BVAR almost always outperforms the conventional BVAR and the naïve forecast (relative RMSE < 1) for most variables.
  - Exception: lending rate — the mean-adjusted BVAR is consistently outperformed by the naïve forecast (nominal interest rates are highly persistent; lending rate was virtually flat over the sample).

### Unconditional and conditional forecasts through 2010
- Forecast types:
  - Unconditional (endogenous) forecast: model-based.
  - Conditional forecasts:
    - WEO-based conditional forecast: imposes world growth path (IMF Fall 2007 WEO) and U.S. interest-rate path.
    - Downside hypothetical conditional forecast: global growth lower than Fall 2007 WEO by 1 percentage point in each quarter of 2008; U.S. three-month treasury bill rate decreases in response.
- Key forecast outcomes:
  - Unconditional (endogenous) forecast:
    - Growth decelerates to around 4½ percent by end-2008 and stabilizes at about 4 percent in 2009.
  - WEO-based conditional forecast:
    - Growth of about 5¼ percent by the end of 2008 and 4¾ percent in late 2009.
    - Stronger average growth driven by higher WEO world GDP growth projections relative to endogenous forecast.
  - Downside conditional forecast (global growth shock):
    - Colombian GDP growth reaches a low of 3 percent in late 2008Q3 (compared to 4¾ percent under the WEO-based conditional forecast).
    - Under this scenario growth declines to 3 percent, which is 1¾ percentage points below the baseline forecast.
    - EMBI spread increases substantially (not conditioned upon), consistent with historical correlation between U.S. downturns and global risk appetite.
    - Recovery is predicted to be fairly rapid, with growth reaching the same level as in the WEO-based forecast by the end of 2009.
- Interpretation:
  - The model supports that Colombian growth is fairly sensitive to changes in global growth.
  - A moderate global slowdown would produce a substantial domestic slowdown but not a full-blown recession; growth remains positive and the downturn is mild by historical standards.

### Conclusions and policy-relevant findings
- Aggregate findings:
  - Domestic factors explain about 60 percent of Colombian GDP growth variability; external developments explain about 40 percent.
  - Among domestic factors, the investment climate (FDI) and fiscal policy are prominent contributors; monetary policy has had a small contribution.
  - Global economic growth is the single most important external factor for Colombian growth.
  - External financial-condition measures (U.S. interest rate, EMBI, high-yield spreads) each account for only modest shares.
- Policy implications and robustness considerations:
  - Fiscal and monetary policy shocks each have moderate short-run impacts on growth; investment-climate improvements have a moderate positive effect.
  - The model implies a deceleration of economic growth to 4-5 percent in 2008-10, from close to 7 percent in 2006-07.
  - Structural reforms since the early 2000s, higher international reserves, and a flexible exchange rate regime may have enhanced resilience to external shocks, but greater financial integration could increase sensitivity; the net effect remains to be tested.
  - The model’s results are sensitive to sample period and included variables; classification between domestic and foreign influences is imperfect.

*Source: IMF working paper content provided in the input document.*

### References

### _wp0846 - References

### References
- Adolfson, M., M.K. Anderson, J. Lindé, M. Villani, and A. Vredin, 2007, “Modern Forecasting Models in Action: Improving Macro Economic Analyses at Central Banks,” International Journal of Central Banking 3, pp. 111–44.
- Campbell, J.Y. and R.J. Shiller, 1991, “Yield Spreads and Interest Rate Movements: A Bird’s Eye View,” Review of Economics and Statistics 58, pp. 495–514.
- Clarida, R., J. Gali, and M. Gertler, 1998, “Monetary Policy Rules in Practice. Some International Evidence,” European Economic Review 42, pp. 1033–67.
- International Monetary Fund, 2006, Colombia—Staff Report for the 2006 Article IV Consultation and Third and Final Review Under the Stand-By Arrangement. Country Report EBS/06/131. Washington, D.C.
- Loayza, N., P. Fajnzylber, and C. Calderón, 2004, “Economic Growth in Latin America and the Caribbean: Stylized Facts, Explanations and Forecasts,” Working Papers of Central Bank of Chile 265.
- Österholm, P., 2008, “Can Forecasting Performance Be Improved by Considering the Steady State? An Application to Swedish Inflation and Interest Rate,” Journal of Forecasting 27, 41-51.
- Österholm, P. and J. Zettelmeyer, 2008, “The Effect of External Conditions on Growth in Latin America,” Forthcoming in IMF Staff Papers.
- Taylor, J.B., 1993, “Discretion versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy 39, pp.195–214.
- Villani, M., 2008, “Steady State Priors for Vector Autoregressions,” Forthcoming in Journal of Applied Econometrics.
- Villani, M. and A. Warne, 2003, “Monetary Policy Analysis in a Small Open Economy Using Bayesian Cointegrated Structural VARs,” Working Paper No. 296, European Central Bank.
- Zettelmeyer, J., 2006, “Growth and Reforms in Latin America: A Survey of Facts and Arguments,” IMF Working Paper 06/210, International Monetary Fund.

*Source: _wp0846 - References*

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